Lesson Notes By Weeks and Term v4 - JHS 3
Number: Ratios and Proportion
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Number: Ratios and Proportion
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: JHS 3
Term: 2nd Term
Week: 11
Grade code: B9.3.2.1.1
Strand code: 3
Sub-strand code: 4
Content standard code: B9.3.1.2
Indicator code: B9.3.2.1.1
Theme: GEOMETRY AND MEASUREMENT
Subtheme: Number: Ratios and Proportion
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In our daily lives in Ghana, we are surrounded by objects that have specific shapes. Think about the wooden 'chop box' for storing food items, a box of Ideal Milk, or even the shape of some buildings. These are 3D shapes. Today, we are going to explore two of these shapes: the cuboid and the triangular prism. We will learn how to 'unwrap' them into a flat pattern called a net. By understanding these nets, we can figure out the total area needed to cover their entire surface, which is a very useful skill for packaging, painting, and construction.
Part 1: Identifying Prisms and Their Nets What is a Prism? A prism is a 3D solid object with two identical ends (called bases), flat faces, and the same cross-section all along its length. The faces connecting the bases are rectangles. Cuboid (or Rectangular Prism) A cuboid is a prism with rectangular bases. All its faces are rectangles. Think of a standard school textbook, a matchbox, or a rectangular water tank (like a Polytank). Properties: It has 6 faces, 12 edges, and 8 vertices (corners). Triangular Prism A triangular prism is a prism with triangular bases. Think of a Toblerone chocolate box, a camping tent, or a slice of yam cut into a wedge shape. Properties: It has 5 faces (2 triangles and 3 rectangles), 9 edges, and 6 vertices. What is a Net? A net is the 2D pattern you get if you 'unfold' a 3D shape and lay it flat. Imagine you carefully cut along the edges of a Milo tin box and opened it up. The flat piece of cardboard is the net of the cuboid. Part 2: Deriving the Formula for Surface Area using Nets
The Surface Area (SA) of a 3D shape is the total area of all its faces added together. We can find this by calculating the area of each shape in the net and summing them up.
A. Surface Area of a Cuboid
Let's consider a cuboid with length (l), width (w), and height (h). Visualise and Draw the Net: If we unfold the cuboid, we get 6 rectangles. These rectangles come in three pairs of identical sizes: Top and Bottom faces: Both have area = length × width = lw Front and Back faces: Both have area = length × height = lh Left and Right side faces: Both have area = width × height = wh Calculate Total Surface Area: To get the total surface area, we add the areas of all six faces. SA = (Area of Top) + (Area of Bottom) + (Area of Front) + (Area of Back) + (Area of Left) + (Area of Right) SA = (lw) + (lw) + (lh) + (lh) + (wh) + (wh) SA = 2(lw) + 2(lh) + 2(wh)